Question: Factor the following expression: $-6$ $x^2+$ $13$ $x$ $-2$
This expression is in the form ${A}x^2 + {B}x + {C}$ . You can factor it by grouping. First, find two values, $a$ and $b$ , so: $ \begin{eqnarray} {ab} &=& {A}{C} \\ {a} + {b} &=& {B} \end{eqnarray} $ In this case: $ \begin{eqnarray} {ab} &=& {(-6)}{(-2)} &=& 12 \\ {a} + {b} &=& & & {13} \end{eqnarray} $ In order to find ${a}$ and ${b}$ , list out the factors of $12$ and add them together. The factors that add up to ${13}$ will be your ${a}$ and ${b}$ When ${a}$ is ${1}$ and ${b}$ is ${12}$ $ \begin{eqnarray} {ab} &=& ({1})({12}) &=& 12 \\ {a} + {b} &=& {1} + {12} &=& 13 \end{eqnarray} $ Next, rewrite the expression as ${A}x^2 + {a}x + {b}x + {C}$ $ {-6}x^2 +{1}x +{12}x {-2} $ Group the terms so that there is a common factor in each group: $ ({-6}x^2 +{1}x) + ({12}x {-2}) $ Factor out the common factors: $ x(-6x + 1) - 2(-6x + 1) $ Notice how $(-6x + 1)$ has become a common factor. Factor this out to find the answer. $(-6x + 1)(x - 2)$